If anyone hasn't read through Chris Li's blog, I would suggest doing so. Perhaps these two are appropriate more than the others ...
Now, it is interesting to note in the first part, that "Gozo Shioda, who said that 'Ueshiba sensei was always talking about breath power, breath power (kokyu-ryoku)'."
If you read Total Aikido by Shioda, on the section titled "Kokyu-Ryoku" (page 16 in my book), we find:
"Breath power is what is developed at the point where our own focused power comes into contact with the other person. Here the matter of spirit and rhythm (timing) are of basic importance."
Side Note: The parenthetical "(timing)" is not correct here for rhythm. Shioda goes on in the next two paragraphs to define both spirit and rhythm. Spirit is not focusing on a technique, but being "empty" and reading the other person's movements. Rhythm is a result of your own breathing.
Back to the subject. Shioda goes on to state, "When feeling (sensitivity), breathing, and rhythm are brought together and become one, kokyu-ryoku, or breath power, is born. You and the other person become as one: where you lead you will be able to make uke follow."
Side Note: Interesting choice of words - "make uke follow". Not blend, not become one, but you make uke follow. Didn't Ueshiba state aikido is making the other person do what you want?
Back to the subject. You should read Chris' blog posts. Too much in there to actually put here. Basically, breath power is related to concepts that are not actually anything to do with the physical function of breathing. Shioda's words seem to uphold those notions.
It would seem that this "Breath Power" or "Kokyu" or "Kokyu Ryoku" doesn't have much to do with the actual act of breathing.
As students of aikido, how has kokyu, kokyu ryoku, breath throw, breath power, etc been explained to you?